Identifying Linear vs Nonlinear Functions in AP Physics

This video tutorial covers the identification of linear and non-linear functions using tables, graphs, and equations. It explains how to determine if a function is linear by checking for a constant rate of change in tables, a straight line in graphs, and specific properties in equations. The video also provides examples and exercises to practice these concepts, emphasizing the importance of recognizing linearity in different mathematical representations.

What is the primary visual difference between linear and non-linear functions on a graph?

• Linear functions have a straight line.

• Linear functions have a curved line.

• Non-linear functions have a constant slope.

• Non-linear functions have a straight line.

Tags

CCSS.8.F.A.3

How can you identify a linear function using a table?

• The values of y are always decreasing.

• The rate of change varies.

• The rate of change is constant.

• The values of x are always increasing.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

In a table, if the x values increase by a constant amount and the y values decrease by a constant amount, what type of function is it?

• Non-linear

• Quadratic

• Linear

• Exponential

Tags

CCSS.8.F.A.3

What question should you ask to determine if a graph is linear?

• Does the graph have a constant slope?

• Is the graph a horizontal line?

• Is the graph a straight line?

• Does the graph curve upwards?

Tags

CCSS.8.F.A.3

Which of the following graphs represents a non-linear function?

• A curved line

• A straight line going downwards

• A horizontal line

• A straight line going upwards

Tags

CCSS.8.F.A.3

What is the standard equation form of a linear function?

• y = x^2 + c

• y = 1/x + d

• y = mx + b

• y = ax^3 + b

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Why is the equation y = 6/x considered non-linear?

• Because it has a constant slope

• Because x is in the denominator

• Because x is in the numerator

• Because x is raised to the power of 1

Tags

CCSS.8.F.A.3

Which of the following equations is linear?

• y = x^2 + 2

• y = 3x/2 + 1

• y = 2/x + 5

• y = x^3 + 1

Tags

CCSS.8.F.A.3

What is the power of x in a linear equation?

• 2

• 0

• 1

• 3

Tags

CCSS.6.EE.A.2C

What is a key characteristic of a linear function in a table?

• The y values are always negative.

• The rate of change is constant.

• The rate of change is variable.

• The x values are always positive.

Tags

CCSS.HSF-LE.A.1B